Generating function for a chess knight and king on an arbitrarily-dimensioned chessboard
knight(d=2)
king(d=2)Dimensionality of the board, defaulting to 2
Returns the generating function of the piece in question.
# NOT RUN {
## How many ways can a knight return to its starting square in 6 moves?
constant(knight()^6)
## How many in 6 or fewer?
constant((1+knight())^6)
## Where does a randomly-moving knight end up?
d <- xyz(2)
kt <- (1+knight())*d^2/9
persp(1:25,1:25,as.array(d*kt^6))
## what is the probability that a 4D king is a knight's move from
## (0,0,0,0) after 6 moves?
sum(value(((king(4)/80)^4)[knight(4)]))
# }